| Abstract: |
| Total mass, energy and momentum are natural integral characteristics
for many systems of PDEs describing meaningful models - from gas
dynamics to liquid crystals, chemotaxis, self-gravitating gas,
granulated media, economical mean field games, etc. All these
equations have some common structure, which allows us to consider
them as gas-dynamics-like systems. It is possible to introduce
others integral quantities related to momentum of mass and to obtain
a nonlinear ODE system of equalities and inequalities even in
multidimensional case. Analysis of these systems is helpful for many
purposes. It allows to obtain nonexistence result for the solutions
to the Cauchy problem and free boundary problem, study the
propagation of support of solution, and construct special classes of
classical solution. |
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